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    Surge Control in Pumping Stations

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    Surge Control in Pumping Stations

    Surge Control in Pumping Stations

    Surge Control in Pumping Stations

    Written by Val-Matic Valve and Manufacturing Corporation

    This primer presents basic Surge Control principles and the functions of variousvalves associated with Pumping stations.

    Water pipelines and distribution systems are subjected to surges almost daily,which over time can cause damage to equipment and the pipeline itself. Surges arecaused by sudden changes in fluid velocity and can be as minor as a few PSI to five

    times the static pressure. The causes and effects of these surges in Pumpingsystems will be discussed, along with equipment that is designed to prevent anddissipate surges. Reference will be made to typical installations and examples so

    that an understanding of the applicable constraints can be gained. Figure 1illustrates a typical water pumping/distribution system where two parallel pumps

    draw water from a wet well, then pump the water through check and butterfly valvesinto a pump header and distribution system. A Surge tank and relief valve are

    shown as possible equipment on the pump header to relieve and prevent surges.Each of these will be discussed in greater detail.

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    Causes and Effects

    Surges are caused by sudden changes in flow velocity that result from commoncauses such as rapid valve closure, pump starts and stops, and improper fillingpractices. Pipelines often see their first Surge during filling when the air being

    expelled from a pipeline rapidly escapes through a manual vent or a throttled valve

    followed by the water.Being many times denser than air, water follows the air to the outlet at a high

    velocity, but its velocity is restricted by the outlet, thereby causing a surge. It isimperative that the filling flow rate be carefully controlled and the air vented through

    properly sized automatic air valves. Similarly, line valves must be closed andopened slowly to prevent rapid changes in flow rate.

    The operation of pumps and sudden stoppage of pumps due to power failuresprobably have the most frequent impact on the system and the greatest potential to

    cause significant surges. If the Pumping system is not controlled or protected,contamination and damage to equipment and the pipeline itself can be serious.

    The effects of surges can be as minor as loosening of pipe joints to as severe asdamage to pumps, valves, and concrete structures. Damaged pipe joints and

    vacuum conditions can cause contamination to the system from ground water andbackflow situations. Uncontrolled surges can be catastrophic as well. Line breaks

    can cause flooding and line shifting can cause damage to supports and evenconcrete piers and vaults. Losses can be in the millions of dollars, so it is essential

    that surges be understood and controlled with the proper equipment.Surge Background

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    Some of the basic equations ofSurge theory will be presented, so an understandingofSurge Control equipment can be gained. First, the Surge pressure (H) resulting

    from an instantaneous flow stoppage is directly proportional to the change invelocity and can be calculated as follows:

    H = a v / g

    where:H = Surge pressure, ft water columna = speed of pressure wave, ft/sv = change in flow velocity, ft/s

    g = gravity, 32.2 ft/s2The speed of the pressure wave (a) varies with the fluid, pipe size, and pipe material.

    For a medium sized steel line, it has a value of about 3500-ft/s. For PVC pipes, thespeed will be far less. For a 12-in steel line with water flowing at 6-ft/s, the

    magnitude of a Surge from an instantaneous flow stoppage is:H = (3500 ft/s)(6 ft/s) / (32 ft/s2(

    H = 656 ft water columnThis Surge pressure of 656-ft (285-psi) is in addition to the static line pressure;

    therefore, the resultant pressure will likely exceed the pressure rating of the system.Further, this high pressure will be maintained for several seconds as the wave

    reflects from one end of the piping system to the other end, causing overpressurization of pipe seals and fittings. Then after a reflection, the pressure wavemay cause a negative pressure and vacuum pockets for several seconds, allowing

    contaminated ground water to be drawn into the system through seals orconnections.

    Even higher velocities than the Pumping velocity are attainable in long pipingsystems. If the pumps are suddenly stopped due to a power failure, the kinetic

    energy of the water combined with the low inertia of the pump may cause aseparation in the water column at the pump or at a highpoint in the pipeline. Whenthe columns of water return via the static head of the line, the reverse velocity canexceed the normal velocity. The resultant Surge pressure can be even higher than

    the 656-ft calculated above.Transient analysis computer programs are normally employed to predict column

    separation and the actual return velocities and surges. Transient programs can alsomodel methods employed to Control column separation, such as the use of a Surge

    tank, vacuum breaker, or air valve. These solutions will be discussed in greaterdetail.

    Thus far, the changes in velocity have been described as "sudden." How suddenmust changes in velocity be to cause surges? If the velocity change is made withinthe time period, the pressure wave will travel the length of the pipeline and return,

    the change in velocity can be considered instantaneous, and the equation forSurgepressure (S) given earlier applies. This time period, often called the critical period,

    can be calculated by the equation:t = 2 L / a

    where:

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    t = critical period, secL = length of the pipe, ft

    a = speed of the pressure wave, ft/sFor the earlier example of the 12-in line, the critical period would be as follows for a

    4-mi long steel pipeline:t = 2 (21,120 ft) / (3500 ft/sec(

    t = 12 secTo cause surges, a pump does not need to stop quickly nor does the valve need to

    close instantaneously (or even suddenly). A normal flow stoppage of 5 or 10seconds may cause the maximum Surge in long Pumping systems. It follows that

    Surge Control strategies should be employed on all long pipelines.Pumps

    Referring again to Figure 1, a key to controlling surges in Pumping systems is toControl the rate of increase and decrease of the flow velocity into the system.

    Pumps should be sized for the expected flow requirements. Multiple pumps can be

    used to match varying demands for water. Oversized pumps can create havoc incertain Pumping systems.Special pump motorControl systems are available to slowly ramp up and rampdown the pumps by controlling the electrical drive of the pump. These systems

    Control supply and can prevent surges during normal pump operation. However,after a power failure the motor controls become inoperative and the pump will trip

    instantly and cause a sudden stoppage of flow.Some pump station designs employ multiple pumps so that when one of the pumpsis started or stopped, the stopped pump has a minor impact on the overall pipeline

    velocity. However, these Stations are likewise faced with the severe impact of apower failure. Almost all Pumping systems need additional Surge equipment to

    prevent surges after a power failure.Vertical Pumps and Well Service Air Valves

    Vertical pumps, as shown in Figure 2, lift water from a tank or wet well into apipeline. When the pump is off, the suction water level is below the pump discharge

    pipe. The pump column refills with air after each pump stoppage.

    Air valves play an important roll in automatically venting the pump column air and

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    controlling surges in pump columns. If the vertical turbine pump is started withoutan air valve, the air in the pump column would be pressurized and forced through

    the check valve into the pipeline, causing air related problems. Air valves for pumpdischarge service, called well service air valves, are similar to air/vacuum valves but

    are equipped with either a throttling device or anti-slam device, and are designed toexhaust air on pump start-up and admit air upon pump shut down.As shown in Figure 3, the well service air valve is a normally-open, float-operated

    valve which relieves the air in the pump column rapidly. When water enters thevalve, the float automatically rises and closes to prevent discharge of the water.

    Throttling devices are provided on the outlet of 3-in and smaller valves to Controlthe rate of air release, especially with slow opening pump Control valves. The

    throttling device is adjusted with the external screw to slow the rise of the water inthe pump column. However, after pump shutdown, a second port on the top of the

    throttling device provides full flow into the pump column to relieve the vacuum. Thedual port throttling device is important because it provides full vacuum flow and

    prevents contaminated water from being drawn into the pipeline, which can happenif the device has a common exhaust and vacuum connection.

    When a power operated pump Control valve is used with a vertical pump, an airrelease valve equipped with a vacuum breaker can be used, as shown in Figure 4. In

    this case, the pump is started and the opening of the Control valve delayed a fewseconds so that the air release valve can expel the air slowly through its small

    orifice.

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    During the process, the pump column will become pressurized to the pump shutoffhead and force the air out at high pressure. The momentarily trapped air will act as a

    cushion to Control the rise of the water in the pump column. The valve orifice issized to Control the rise of the water to a safe velocity, typically 2-ft/s.

    Check Valves

    Another key element in Pumping system design is the proper selection andoperation of the pump discharge check valve. Every pump station designer hasbeen faced with check valve slam, which is caused by the sudden stoppage of

    reverse flow through a closing check valve.To prevent slam, the check valve must either close very quickly or very slowly.Anything in the middle is no-man's land and a cause for concern. But just as

    important, the valve should protect the Pumping system and piping from suddenchanges in velocity if it is within its functional capabilities. The check valve should

    also be reliable and offer low headloss.

    Two categories of check valves will be discussed in detail. The first, fast-closingcheck valves, represent the general category of check valves that operateautomatically in less than a second and without the use of external power or signals

    from the Pumping system. The other category is pump Control valves, whichoperate very slowly (i.e. 60 to 300 seconds) to carefully Control the changes in

    pipeline fluid velocity.Fast-Closing Check Valves

    Fast-closing check valves are simple, automatic, and cost effective, but are often

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    plagued with the problem of check valve slam and a resultant system pressuresurge. If the deceleration of the forward flow can be estimated, such as with a

    transient analysis of the Pumping system, the slamming potential of various checkvalves can be predicted. Then, several non-slam valve options will present

    themselves, and the performance features and costs can be used to select the best

    check valve for the application.The most ubiquitous type of check valve is the traditional swing check valve. Swingcheck valves are defined in AWWA C508 for waterworks service and are designed to

    rapidly close to prevent backspinning of the pump during flow reversal.Traditional swing check valves have 90-deg seats with long strokes and are subjectto slamming. These valves are therefore outfitted with a wide array of accessories,

    which are beyond the scope of the AWWA C508 Standard. Probably the mostcommon accessory is a lever and weight. While it is normally assumed that the

    weight makes the valve close faster, it actually reduces slamming by limiting thestroke of the disc, but in return, causes a significant increase in headloss. The valveclosure is also slowed by the inertia of the weight itself and the friction of the stem

    packing.

    In more severe applications, an air cushion is sometimes used to slow down theimpact of the valve closure. Everyone has seen how effective an air cushion works

    on a slamming storm door. But the conditions in a pipeline are significantly different.

    When a door slams, its momentum is smoothly absorbed by the air cylinderbecause as the door slows, the forces from the closing spring and outside wind

    become less and less. Conversely, when a check valve in a pipeline closes, thereverse flow is quickening at a tremendous rate, so every fraction of a second that

    the valve closure is delayed, the forces on the disc will increase by an order ofmagnitude.

    While it may be true that an air cushion prevents the weight from slamming the discinto the seat of a valve in a product display booth, in actual practice, the air cushionmerely holds the disc open long enough for the reverse flow to intensify and slamthe disc even harder into the seat. Since air cushions are based on the use of air

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    )which is compressible), they provide no positive restraint of the closing disc andcannot counteract the enormous forces being exerted by the reverse flow. In sum,the best setting of an air cushion is typically where the discharge needle valve is

    fully open and the air is expelled at the highest rate.A far more effective accessory for controlling swing check valve motion is an oilcushion, also referred to as an oil dashpot. Because oil is incompressible, the oilcushion will withstand the high forces exerted on the disc by the reverse flow andproperly Control the last 10 percent of valve closure. The pump must be capable of

    some significant backflow, though, because the oil dashpot will allow the checkvalve to pass a portion of the flow back through the pump.

    Since the reverse flow forces on the valve disc are extremely high, the oil pressureoften exceeds 2000-psig, causing valves with these devices to be costly. The high-

    pressure oil cylinder is expensive and because it puts the valve stem under highloads, a special check valve is often needed. Because pumps can only withstand somuch backflow, the closure time of dashpots are usually limited to 1 to 5 seconds. Ifthe pipeline contains debris or sewage, a check valve with oil cushion can act as a

    screen during reverse flow conditions and quickly clog the line.An even better solution is to select a check valve that closes before any significant

    reverse flow develops, thereby preventing a slam. One such valve is a spring-loaded, center-guided "silent" check valve (SCV) as shown in Figure 6. An SCV is

    near slam-proof because of its short linear stroke (1/4 diameter), location of the discin the flow stream, and strong compression spring. However, selecting a Silent

    Check Valve has several pitfalls such as high head loss, no position indication, andlimitation to clean water applications.

    On the other end of the spectrum is a Tilted Disc check valve (TDCV). The TDCV asshown in Figure 7 has the lowest headloss because its port area is 140 percent of

    pipe size and its disc is similar to a butterfly valve disc where the flow is allowed topass on both sides of the disc. This valve has reliable metal seats and can be

    equipped with top or bottom mounted oil dashpots to provide effective means ofvalve Control and Surge minimization. It is fully automatic and requires no external

    power or electrical connection to the pump control.Another option is a resilient disc check valve, called a Swing-Flex check valve

    )SFCV). The only moving part of the SFCV is the flexible disc. This valve has a 100percent port slanted at 45-deg, which provides a short 35-deg stroke, quick closure,and low head loss. It is also available with a mechanical position indicator and limitswitches. The Surgebuster (SB) has an even faster closure due to the addition of aDisc Accelerator giving the SB closure characteristics similar to a silent check valve

    .

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    With all of the check valve possibilities, one is available for every system with lowhead loss and slam-free operation. The closing characteristics of all types of checkvalves are shown for various system decelerations in Figure 9. The valves whose

    curves are furthest to the right have the best non-slam characteristics.

    Pump Control Valves

    Even though a fast-closing check valve may prevent slam, it may not fully protectPumping systems with long critical periods from velocity changes during pumpstartup and shutdown. ForPumping systems where the critical period is long, a

    pump Control valve is often used.A pump Control valve is wired to the pump circuit and provides adjustable openingand closing times in excess of the system critical time period. Pump Control valvesare hydraulically operated so the motion of the closure member of the valve (i.e. a

    butterfly valve disc) is unaffected by the flow or pressure in the line. Also, mostpumps in service today have low rotating inertia and come to a stop in less than 5seconds.

    The pump Control valve can close rapidly during power outages or pump trips toprotect the pump. However, when rapid closure is required, additional Surge

    equipment will be needed, as explained in the following section. First, though, theselection criteria pertaining to pump Control valves will be presented.

    The list of possible pump Control valves is long because many valves can beequipped with the automatic controls necessary forPumping systems. Valvestypically considered are butterfly, plug, ball, and globe-pattern Control valves.

    Probably the most common criterion used to select a valve is initial cost, but forPumping systems, the selection process should be carefully undertaken with

    consideration given to:

    zvalve and installation costszpumping costs

    zseat integrityzreliability

    zflow characteristics

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    The installed costs for the various types of pump Control valves can vary widely.For example, a 12-in butterfly or plug valve with a hydraulic powered actuator andcontrols can cost $5,000, while a ball valve or globe-pattern Control valve can be 2times to 4 times that amount. In addition to the purchase cost, the cost for makingthe flange connections, Control wiring to the pump motor controls, and providing

    concrete pedestals for the heavier ball and globe-pattern Control valves should alsobe added.Of course, the installed cost of the valve is important and represents an importantinvestment. But equally important is the Pumping cost associated with the head

    loss through the valve. The electrical current draw of the pump is a function of thesystem head loss and flow rate. The additional electrical costs due to valve

    headloss can be calculated using the formula:A = (1.65 Q H Sg C U) / E

    where:A = annual energy cost, dollars per year

    Q = flow rate, gpmH = head loss, ft of water

    Sg = specific gravity, dimensionless (water = 1.0(C = cost of electricity, $/kWhr

    U = usage, percent x 100 (1.0 equals 24 hrs per day(E = efficiency of pump and motor set (0.80 typical(

    For example, the difference in headloss between a 12-in butterfly valve (K = .43) anda globe-pattern Control valve (K = 5.7) in a 4500-gpm (12.7-ft/s) system can be

    calculated as follows:H = K v2 / 2 g

    where:H = headloss, ft water column

    K = flow resistance coefficient, dimensionlessv = velocity, ft/s

    g = gravity, 32.2 ft/s2substituting:

    H = (5.7 - 0.43) (12.7)2 / 232.2=13.2ft. wc

    This difference in headloss can then be used to calculate the difference in annualoperating costs, assuming an electricity cost of $.05 per kW-hr and 50 percent

    usage.

    A = (1.65 x 4500 x 13.2 x 1.0 x 0.05 x 0.5) / (0.8(=$3,062

    The calculation shows that the use of a 12-in butterfly valve in the place of a 12-inglobe-style Control valve can save $3,062 per year in energy costs. If the pump

    station had four such valves operating for forty years, the total savings would beabout $490,000 over the life of the plant. It is clear that Pumping costs can be even

    more important than the installed costs. Further, the larger the valve, the greater theimpact from the energy costs.

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    Typical headloss flow factors are shown in the table below, in order of lowerheadloss. The AWWA ball valve has the lowest headloss of all pump Control valves,but the AWWA butterfly valve probably provides the best balance between energy

    costs and installation costs.12-in Valve Flow Data

    TYPE OF VALVEPORT SIZECvK

    Globe-Pattern Control Valve100%

    1,8005.70

    Silent Check Valve100%

    2,5002.95

    Dual Disc Check Valve80%

    4,0001.15

    Swing Check Valve*100%

    4,2001.05

    Eccentric Plug Valve80%

    4,7500.81

    Swing-Flex Check Valve100%

    4,8000.80

    Tilted Disc Check Valve140%

    5,400

    0.63Butterfly Valve

    90%6,5500.43

    Ball Valve100%

    21,500

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    0.04The integrity of the pump Control valve seat is also important so that the pump canbe serviced without backflow through the valve. A resilient seat in the valve, which

    mates with a corrosion resistant seating surface, is highly reliable because itprovides zero leakage. If any leakage is allowed, such as with ill-fitting metal seats,debris will build up at the leakage sites and the mating surfaces can be subject to

    erosive wear from debris or high velocity leakage.To be reliable, the valve should be built and proof-of-design tested to industry

    standards such as AWWA C504, Butterfly Valves, published by the American WaterWorks Association, to assure reliability in design as well as performance. Some

    valves such as globe-pattern Control valves are not covered by an AWWA standard.

    Finally, the flow characteristics of pump Control valves will determine how well theywill prevent surges. The most desirable flow characteristic of a valve is one wherethe valve uniformly changes the flow rate when installed in the system. The flowdata available from valve manufacturers are inherent flow characteristics usually

    expressed in terms of a flow coefficient (Cv) at various positions, as shown inFigure 10.

    On the left side is a quick-opening valve curve (such as a swing check valve), whichdepicts a rapid change in the flow rate as the valve opens. On the other extreme isan equal percentage valve (such as a V-ported ball valve), which changes the flow

    rate at a uniform percentage. The most desirable flow characteristic for longpipelines is equal percentage as provided by butterfly and ball valves.

    All of the selection criteria discussed, including cost, headloss, reliability, and flowcharacteristics, should be considered together when selecting a valve. No singlevalve type will excel in all categories. The benefits of the expected performance

    must be weighed against the costs and impact on the system Surge potential. Pump Control Valve Operation

    Utilizing a butterfly valve, let us consider the operation of a typical pump Controlvalve. A butterfly valve is operated by rotating its shaft 90-deg and is normallyequipped with a hydraulic cylinder actuator. The cylinder can be powered with

    pressurized water from the line or from an independent oil power system.We learned earlier that negative Surge conditions can occur for several seconds, so

    a backup water or oil system is appropriate. Figure 11 illustrates a typical

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    installation. Hydraulic controls electrically wired into the pump circuit are mountedon the valve. Four-way and two-way solenoid valves (SV) direct the operating

    medium to the cylinder ports to cycle the valve. The speed of opening and closing iscontrolled by independently adjustable flow Control valves (FCV). Flow Control

    valves are special needle valves with a built-in reverse check valve to allow free flow

    into the cylinder but controlled flow out of the cylinder.

    When the pump is started and pressure builds, a pressure switch (PS) located onthe pump header signals the butterfly valve to open. During shutdown, the valve is

    signaled to close while the pump continues to run. When the valve nears the closedposition, a limit switch (LS) located on the valve will stop the pump.

    The safe operating time for the pump Control valve is usually much greater than thecritical period. A long operating time is needed on pipeline applications because thevalve's effective closing time is a fraction of its total closing time due to the fact thatthe valve headloss must be combined with the total pipeline headloss in controllingthe flow rate. Initial field settings will normally be three to five times greater than the

    critical period to minimize the surge.One additional function of the pump Control valve should be considered: prevent

    the pump from backspinning after power failure or overload trip. Since pumps todayare no longer equipped with flywheels, as with old diesel units, they have a low

    rotating inertia and come to rest in a just a few seconds. Therefore, after a poweroutage or pump trip, the pump Control valve must close more rapidly to prevent

    backspinning.The valve hydraulic controls are equipped with a bypass line equipped with a 2-way

    solenoid valve (SV) to send the controlled cylinder flow around the normal flowControl valve and through a large flow Control valve (FCV), thereby closing thepump Control valve automatically in 5 to 10 seconds after power failure. This is

    essential to prevent excess pump backspin and to prevent depletion of the hydro-pneumatic Surge tank water back through the pump if one is utilized.

    As an alternative to the special bypass circuit, a fast-closing check valve issometimes installed upstream of the pump Control valve to back-up the Controlvalve. The fast-closing check valve not only prevents reverse flow through the

    pump, but also provides redundant protection of the pump should the pump Controlvalve fail to close due to loss of pressure or equipment malfunction.

    The rapid closure of either the pump Control valve or a fast-closing check valve in a

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    long piping system poses a dilemma. It was previously explained that the Controlvalve should close in three to five times the critical period. On the other hand, thevalve must close in five seconds to protect the pump after a power failure. Hence,

    on these systems, excessive surges will be caused on power outages so additional

    Surge protection is usually needed.Surge Relief Equipment

    Since it is impractical to use pipe materials, which can handle high Surge pressuresor slow the operating flow velocity to a crawl, Surge relief equipment is needed to

    anticipate and dissipate surges from sudden velocity changes after power outages.Surge relief equipment will also provide protection against malfunctioning valves,

    improper filling, or other system problems.Standpipes and Surge Tanks

    Many types ofSurge relief equipment are used to safeguard Pumping systems. Forlow-pressure systems, a standpipe open to atmosphere will relieve pressure almost

    instantly by exhausting water. For systems with higher pressure, the height of astandpipe would be impractical, so a bladder-type accumulator orSurge tank with

    pressurized air over water can be used to absorb shocks and prevent columnseparations (see Figure 12(.

    )FIGURE 12) Hydro Pneu Surge Tank.eps

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    When a pump suddenly stops, the pressure in the header will drop below the staticpressure and trigger the Surge anticipator valve to open. The valve will then be

    partially or fully open when the return pressure Surge occurs. Anticipator valvestypically open in less than five seconds, pass high low rates, and reclose slowly atthe pump Control valve closure rate (60 to 300 seconds). The sizing ofSurge relief

    valves is critical and should be overseen by transient analysis experts.Anti-Slam Combination Air Valves

    Air valves help reduce surges in pipelines by preventing the formation of airpockets in pipelines during normal operation. Air pockets can travel along a

    pipeline and cause sudden changes in velocity and adversely affect equipmentoperation, such as flow measuring devices. Air valves are also designed to openand allow air to be admitted to the pipeline to prevent the formation of a vacuum

    pocket associated with column separation. Transient analysis computer programsare equipped to analyze the Surge reduction from using various size air valves.

    When column separation is expected at the air valve location, the air valve shouldbe equipped with an anti-slam device which controls the flow of water into the air

    valve to prevent damage to the valve float (see Figure 14(.

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    The anti-slam device allows air to pass through it unrestricted during either the airdischarge or air re-entry cycle. When water (because of its greater density) enters

    the device, the disc will rapidly close and provide slow closure of the air valve float.The disc contains ports, which allow water to flow through the anti-slam device

    when closed to fill the air valve at about 5 percent of the full fill rate, preventing theair valve from slamming closed.

    Vacuum Breaker Valves

    Another type of air valve used at critical points in the pipeline where columnseparation may occur is a vacuum breaker (VB) (see Figure 15(.

    )FIGURE 15) VB & AR.eps

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    and trapped in the pipeline after a pump trip. The air is then slowly released over afew minutes through the adjoining air release valve, which has a small (i.e. -in)orifice. Again, transient analysis programs are designed to model this type of air

    valve solution as well.References

    z

    American Water Works Association, Steel Water Pipe: a Guide for Design andInstallation M11, "Water Hammer and Pressure Surge", 4th ed. 2004, pp. 51-56.

    zBosserman, Bayard E. "Control of Hydraulic Transients", Pumping StationDesign, Butterworth-Heinemann, 2nd ed., 1998, Sanks, Robert L., ed., pp. 153-

    171.zHutchinson, J.W., ISA Handbook ofControl Valves, 2nd ed., Instrument Society

    of America, 1976, pp. 165-179.zKroon, Joseph R., et. al., "Water Hammer: Causes and Effects", AWWA Journal,

    November, 1984, pp. 39-45.zVal-Matic Valve & Mfg. Corp, 1993 "Check Valve Selection Criteria", Waterworld

    Review, Nov/Dec 1993, pp. 32-35.zRahmeyer, William, 1998. "Reverse Flow Testing of Eight-Inch Val-Matic Check

    Valves", Utah State University Lab Report No. USU-609, Val-Matic Valve TestReport No. 117, Elmhurst, IL, [Confidential[.

    zTullis, J. Paul, Hydraulics of Pipelines, 1984 Draft Copy, Utah State University,pp. 249-322.

    zVal-Matic Valve & Mfg. Corp., "Dynamic Characteristics of Check Valves", 2003.

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